Ms Harman - who is known for her campaigning on women's rights - said the next Speaker must be "scrupulously neutral" on debates, and praised Mr Bercow.

She told Today: "This is a Parliament in very difficult times. We have got very divided times in the country and Parliament itself is divided.

"I think what Parliament has to do, and the Speaker has to do, is to ensure that Parliament can have its say... and that is what John Bercow has sought to do."

Asked if she would be able to remain neutral in the chair, Ms Harman said: "Once you offer yourself for election as Speaker, you are making a promise you will set [your party] aside and be neutral, so whoever [is Speaker] will have to go through that transition.

"I would be a champion for Parliament.

"I think the relationship between Parliament and public is very difficult at the moment, and I think a really confident, positive voice speaking about the importance of Parliament with the public is necessary at this time."

Who is Harriet Harman?

Image copyrightGetty ImagesImage caption
Harriet Harman on the campaign trail in 1982 with then shadow home secretary Roy Hattersley

Harriet Harman became the MP for Peckham (later Camberwell and Peckham) during a by-election in 1982 and has remained in her seat ever since.

She went to the exclusive St Paul's Girls' School in London and read politics at York University, before training as a solicitor.

She was rapidly promoted during Labour's years in opposition in the 1980s and 1990s, before becoming Tony Blair's secretary of state for social security and minister for women.

Despite being sacked over welfare reform, she returned to government in 2001 as solicitor general, then secretary of state at the department for constitutional affairs, and, under Gordon Brown, became deputy leader.

She has a reputation as a steely feminist, once joking she was unlikely to become prime minister as there was not enough space at airports for the men who would try to leave the country.

She is married to fellow Labour MP Jack Dromey and has three children.

The news comes after Mr Bercow announced he would be standing down as Speaker at the next general election, or at the end of business on 31 October (Brexit deadline day) - whichever comes first.

In an emotional speech to the Commons, Mr Bercow said his 10-year "tenure" was nearing its end and it had been the "greatest honour and privilege" to serve.

He has faced fierce criticism from Brexiteers, who have questioned his impartiality on the issue of Europe and claim he has facilitated efforts by MPs opposed to a no-deal exit to take control of Commons business.

He has also been criticised for not doing more to tackle allegations of bullying and harassment in the House of Commons - facing accusations himself about mistreating several members of his own staff, which he denies.

Media playback is unsupported on your device

Media captionIn full: Speaker Bercow announces resignation

Who else is running to be the next Speaker?

Harriet Harman is not the only one to put her name forward to become the next Speaker of the Commons when Mr Bercow steps down.

So who are the other candidates?

Sir Edward Leigh - Conservative MP for Gainsborough since 1983

Image copyrightAFP/Getty

Sir Edward became the first MP to explicitly make a pitch to be the next Speaker, releasing a statement and a series of tweets on 25 April 2019.

He said he intended to stand when the vacancy comes up, saying that he would be "a traditional speaker who does not speak much".

He added: "Like a judge I would, by my conduct and dress, submerge my personality into the office. I would be rigidly impartial."

She revealed her intention on 28 February 2018, also in The House magazine, saying she would try for Speaker when Mr Bercow "finally decides to go".

She said: "I am fortunate to have had five years' experience in the Speaker's chair. There is a lot to be done to take our democratic system onto the next stage."

She has also talked about her desire to make Parliament more representative, particularly in its representation of mothers.

Pete Wishart - SNP MP for Tayside since 2001, then Perth and North Perthshire since 2005

Image copyrightUK Parliament

Mr Wishart followed in Sir Edward's footsteps to make his announcement on Twitter, but with a manifesto to bring "the Commons into the 21st century".

His pledges include electronic voting, to allow MPs to wear what they like to the Commons and to stop using "honourable member" and "right honourable member" to address people.

He also wants Parliament to move around the UK, rather than just staying put in Westminster.

Lindsay Hoyle - Deputy Speaker and Labour MP for Chorley since 1997

After Mr Bercow announced he was stepping down on Monday, his deputy took to Twitter to announce his candidacy.

He said that MPs are "clearly in unprecedented times", saying it would be "vital to have an experienced Speaker who can provide the stability and leadership the House of Commons requires in order to remain at the centre to our political system".

Mr Hoyle said he had proved himself to be "independent and fair" and had "ensured all members of Parliament have been able to exercise their right to speak on behalf of constituents to hold the government to account - regardless of position or length of service".